Under the Spell of Landau

When Theoretical Physics was Shaping Destinies

Mikhail Shifman

• Publisher: WSPC
• Year: 2013
• ISBN:
  9789814436588
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

This invaluable collection of memoirs and reviews on scientific activities of the most prominent theoretical physicists belonging to the Landau School — Landau, Migdal, Zeldovich, Smorodinsky, Ter-Martirosyan, Kirzhnits, Gribov, Larkin and Anselm — are being published in English for the first time.

The main goal is to acquaint readers with the life and work of outstanding Soviet physicists who, to a large extent, shaped theoretical physics in the 1950s–70s. Many intriguing details have remained unknown beyond the “Iron Curtain” which was dismantled only with the fall of the USSR.

Contents:

• Lev Landau
• Arkady Migdal
• Yakov Zeldovich
• Yakov Smorodinsky
• Karen Ter-Martirosyan
• David Kirzhnits
• Vladimir Gribov
• Anatoly Larkin
• Alexei Anselm
• Time and Destinies
• Some Details for Experts

Readership: Students and teachers of physics in high schools and colleges.

PART I

CHAPTER 1

Lev Landau (left) and Pyotr Kapitsa.

For technical reviews see pp. 451 and 465.

LEV DAVIDOVICH LANDAU^*

BORIS IOFFE
Institute of Theoretical and Experimental Physics
B. Cheremushkinskaya 25, Moscow
117259, Russia
[email protected]

Landau’s Theoretical Minimum

I’ll start with how I became a student of Landau. In my third year at the physics department of Moscow State University I realized I wanted to be a theorist, but doubted whether I was sufficiently talented. It seemed to me that David Kirzhnits, who studied in the same group as me, had more talent than me and could be one, but whether I could was unknown. Still, after some thought I signed up and was enrolled in the theory group. But the department of theoretical physics was weak (I knew this even then, in 1947): all the high-level theorists – Landau, Tamm, Leontovich – had been pushed out of it. Yet along the lines of Marxist-Leninist philosophy great experts remained, hostile to quantum mechanics and relativity. As my classmate Gertsen Kopylov said in his poem “Eugene Stromykin”:

I was there when Lednev,^a

Gathering the professors’ qahal

Kicked with an intrepid toe

At Einstein, the lion gone senile.

And so, in the summer of 1947, I summoned all my courage and took a decisive step: I phoned Landau^b and asked if I could start taking his theoretical minimum exam. He told me to come by in the next few days. I passed the entrance exam in mathematics rather easily, and Landau gave me a typewritten program of the seven other exams (in fact there was also an eighth, mathematics II: complex variables, special functions, integral transforms, etc.). At that time the only books out yet in the Landau course were Landau-Pyatigorsky’s Mechanics, Landau-Lifshitz’s Field Theory, Mechanics of Continuous Media and the first (classic) part of Statistical Physics. All the other courses required study of various books and original articles, in many cases. The articles were in English and German; for instance, in the course on quantum mechanics there were two large articles – 100 pages apiece – by Bethe, from Annalen der Physik. That is, it went without saying that the exam-taker knew both languages.

The exam took place as follows. A student would call Landau and say he wanted to take a test for a certain course (the order of testing for courses was more or less arbitrary). “Fine, come at this or that time.” The visitor had to leave any books, notes, etc. in the hallway. Then Landau invited him into a small second-floor room containing a round table with several sheets of blank paper, a chair and nothing else. Landau formulated the problem and left, but every 15 to 20 minutes he came and looked over the exam-taker’s shoulders to see what was done. If he kept silent, that was a good sign, but sometimes he said “Hmm” – and that was a bad sign. I have no personal experience of what happened in those cases when a student failed an exam. (I only know that re-testing was permitted.) I approached the dangerous line only once, while taking the statistical physics exam. I started solving a problem differently than Landau expected. Landau came up, peered over my shoulder, said “Hmm” and left. After 20 minutes he came back, took another peek and said “Hmm” in a still more displeased tone. Then Lifshitz dropped by on some business. He also had a look at my notes and yelled, “Dau, don’t waste time, get him out of here!” But Dau disagreed: “Let’s give him another 20 minutes.” During this time I got an answer, and the answer was correct! Dau saw the answer, took another look at my calculations and acknowledged I was right. He and Lifshitz asked me a few simple questions, and the exam was passed.

The problems Landau assigned could be quite complex, and the student had to solve each of them in about an hour. (Typically the exam included one or two complex problems and a single easier one.) So exam preparation required a lot of practice in solving problems. To get this practice, I tried to find problems wherever I could. (After all, there were no problem books or collections of the problems now available in Landau’s Course in question form.) I asked Abrikosov, who had passed the theoretical minimum ahead of me, what problems he’d gotten – but not their solutions! – and I solved them. After several exams I discovered that Landau had a fairly limited supply of problems – sometimes he gave me the same problems he’d given Abrikosov. I think Landau realized that the exam-takers were telling each other which problems he assigned, but this didn’t bother him: to assess a student’s capabilities and knowledge, it was enough for him to see how a problem was solved. Here’s an example: a question on macroscopic electrodynamics. A dielectric ball with electric and magnetic susceptibilities ε₁ and μ₁ rotates with angular frequency ω in a medium characterized by ε₂ and μ₂ in a constant electric field

. The angle between the axis of rotation and vector

is equal to α. Find the electric and magnetic field inside the ball and in the medium.

Now here’s an episode to characterize the level of teaching at the university compared to Landau’s minimum. In spring 1948 it was time to take the exam on quantum mechanics at the physics department. The course was lectured by Blokhintsev, but I didn’t attend his lectures. I studied quantum mechanics based on the minimum’s program and figured my level still wasn’t good enough to take the exam with Landau: I still had a lot of work to do. Once in the university courtyard I met Dmitry Shirkov, who was a student at the theory department.

“I’m going to take the early quantum mechanics exam with Blokhintsev. Do you want to join in?”

“Let’s go,” I said after a moment’s reflection.

We passed the exam; I got a five, Shirkov a four.^c But I could only pass the exam with Landau in September, after another three months of preparation.

Passing the minimum took me almost two years. (During the same two years I did two scientific works advised by Pomeranchuk (Chuk).) In June 1949, after I passed the last exam, Landau included me in the list of his students.

Not long – about two or three weeks – before the tragic car accident on January 7, 1962, that ended his creative life, Landau made a list of everyone who had passed the theoretical minimum. For the first twenty years, Landau held all the exams himself. However, since the number of people who wanted to take the minimum exam picked up sharply in the 1950s, sometime in 1954 or 1955, Landau decided to start holding only the first entrance exam in mathematics himself and have the rest held by his team from the Institute of Physical Problems (IPP) – Lifshitz, Khalatnikov, Abrikosov, Gorkov and others. Now, after many years, looking at this list, it is possible to say with certainty who among those who passed the theoretical minimum really achieved significance as a theoretical physicist and who stayed at an average level. And it so happens that a rather sharp boundary shows up around 1954-1955: there are significantly more well-known theorists on the left half of the sheet than on the right. A thought comes to my mind that the important thing was not only the content of the theoretical minimum and the selection of exam problems: there was importance in the role of the examiner. Probably during the exam Landau could see who was really talented and who wasn’t. His students apparently had a harder time in this. Well ... a great person is beyond replication.

But Landau too sometimes permitted loopholes. Absent from the list of who passed the theoretical minimum exam is V. Khozyainov, who passed it in 1950 (or 1951). And this wasn’t forgetfulness on Landau’s part. Khozyainov studied at the physics department in the same class as me, but was older. During allocation among departments he didn’t go into theory, but applied to some other department and was enrolled there. But when several students (myself included) transferred from the theory department to the “Structure of Matter” department (more on this below), the physics department administration decided the theory department needed reinforcement. “Reinforce” always also meant “reinforce politically.” Khozyainov and another student were transferred to the theory department by special order. Khozyainov was a [Communist] Party member, perhaps even a member of the physics department’s Party Committee. That’s how he became a theorist.

That he later passed Landau’s minimum surprised me greatly. I found out about this from Landau himself. Landau added that he planned to accept Khozyainov in the graduate program. I tried to talk him out of this, telling him how Khozyainov had gotten into theory and that I thought Khozyainov was weak as a physicist and personally rather shady. But this had no effect on Landau, and he gave one answer to all my arguments: “He passed the minimum!”

After some time (probably a year and a half to two years later), Landau gave me Khozyainov’s dissertation and asked for my opinion. The dissertation was on particle physics, but formal (I don’t recall its contents), and I assessed it rather sourly. Landau asked, “Is there any nonsense in it? It doesn’t contradict anything?” “No,” I answered, “but there’s not much content.”

“Never mind, – said Landau. – Then it can be defended.”

Khozyainov finished his defense, then commenced his zealous activities. Within a short time he became secretary of the Party Committee of the Institute of Physical Problems. Remember, this was 1952 – the height of anti-cosmopolitanism,^d that is, simply the height of the anti-Semitic campaign. In the IPP theory department headed by Landau the percent of Jews exceeded all permissible norms. In fact, in the department (besides Khozyainov) there was only one Russian (based on his passport): Alexey Abrikosov, who actually was half-Jewish. To rectify this situation, the IPP authorities created a second theory department headed by V. A. Fock.^e Fock greatly disliked this role, but apparently couldn’t refuse. Khozyainov, as the Party committee secretary, took energetic action to replace Landau with Fock as the head of the entire theory department. (Conceivably, though, it wasn’t his initiative and he was only charged with carrying it out.) But his time for success ran out: Stalin died. A short time later, Khozyainov was fired from IPP. Landau never mentioned him again.

Landau’s Seminar

Being Landau’s student was a title that came with no privileges, just duties, since anyone could have scientific discussions with Landau and get his advice. Only a few of those who passed the minimum became his graduate students. The right and simultaneously the responsibility of a Landau student was full-fledged participation in his seminar. But, again, anyone could participate in the seminar, ask questions and make comments. The duties of “full-fledged” seminar members comprised regularly making summary reports in alphabetical order at the seminar. After each seminar, Landau took the most recent issue of Physical Review (the journal wasn’t divided into sections then) and marked the articles the next speaker was to report on at the seminar. Typically there were 10 to 15 articles from very diverse branches of physics. Mainly these were experimental or halfexperimental, half-theoretical articles. Sometimes there were short theoretical articles, such as letters to the editor. I remember how I gave an account of a Physical Review letter to the editor from Marshak and Tamor which presented the results of calculations of photoproduction of muons on the nucleon and the capture of muons in hydrogen in perturbation theory.

The speaker not only had to summarize the article, i.e., present its basic idea and primary results, but also clearly understand how these results were obtained, cite all the necessary formulas and even experimental techniques and explain them to the audience. Most importantly, the speaker had to have his own opinion as to whether a given work was correct. In short, speakers bore the same responsibility for the works they reported on (and for these works’ errors!) as the authors. That held true for works in the most diverse of physics fields, from elementary particle physics and nuclear physics to the properties of metals and liquids.

Landau had a special love for alum. He always marked articles on the properties of alum in Physical Review. So for us (at ITEP) “alum” became a catch-all word to refer to any less-than-interesting Landau seminar topic. (But I reported on alum-related articles conscientiously.) Landau knew each report topic thoroughly (despite the fact that he scarcely read any articles at all, only listened to their presentations) and asked questions requiring immediate and definite answers: generalities like “the author argues that...” were forbidden. The audience always included experts in the field, and they also asked questions and made comments. So making a survey of Physical Review was no easy task. Fortunately, this had to be done about twice annually.

Sometimes, if Landau thought the speaker hadn’t given a sufficiently qualified account of the article, he interrupted him and asked him to go on to the next one. If this happened two or three times in the course of the report, Landau would exclaim:

“You didn’t prepare for the lesson! Who’s next, Alyosha?”

Alexei Abrikosov, the seminar’s secretary, was charged with following the list of speakers. In the worst case, if the same speaker was driven from the podium a few times, he faced ostracism: he was omitted from the list of participants and Landau refused to discuss anything with him, but of course he could still attend the seminar. I recall two such cases, and in one of them the speaker was the wellknown physicist V. G. Levich, a future corresponding member of the Academy of Sciences. Other Landau students were also sub jected to ostracism: Berestetsky, Ter-Martirosyan and even Pomeranchuk, but for different grievances, not for failings at the seminar. I’ll tell of this later. Only after much time had elapsed – about a year or even more – and only after one or two of the more respected participants had interceded for him, would the offender receive a pardon.

Theoretical works were presented differently. A person, not necessarily a seminar participant, who wanted to speak at the seminar about a theoretical work (his own or from the literature) started by describing it to Landau. If Landau agreed with its main propositions, the report was included in the seminar. During the report Landau made clarifying remarks, and quite often his explanations of the work strongly differed from the author’s perspective. A noisy debate ensued. Landau could often be heard to say:

“The author himself doesn’t understand what he’s done!”

In all cases Landau had a completely original understanding of the work, and it wasn’t easy for a typical person to follow his reasoning. I wasn’t the only one to find it took several hours, sometimes days, for me to understand the depth of his statements, which often shed light on a problem from a completely different side.

A theoretical report freed a seminar participant from mandatory surveys of Physical Review. Pomeranchuk, for instance, never made the surveys and always reported on theoretical works. Reports on theoretical works were made not only by physicists from the Landau school but also by Tamm, Bogolyubov, Gelfand and many others. In the postwar period and until 1955 not one foreign physicist ever came to Moscow.

Among the seminar participants were two exceptional people who didn’t fit the usual rules: Ginzburg and Migdal. Landau once said of Ginzburg, “Ginzburg isn’t my student, he just stuck to me.” And indeed, Ginzburg thought of himself as a student of Tamm. Nonetheless, he was one of the Landau seminar’s most ac...

Table of contents

• Front Cover
• Half Title
• Title Page
• Copyright
• Contents
• From the Editor M. Shifman
• PART I
• PART II
• Index